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Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations

Published online by Cambridge University Press:  15 October 2010

A. TOFFOLI ,
O. GRAMSTAD ,
K. TRULSEN ,
J. MONBALIU ,
E. BITNER-GREGERSEN  and
M. ONORATO
A. TOFFOLI*
Affiliation:
Det Norske Veritas, Veritasveien 1, NO-1322 Høvik, Norway
O. GRAMSTAD
Affiliation:
Department of Mathematics, University of Oslo, PO Box 1053 Blindern, NO-0316 Oslo, Norway
K. TRULSEN
Affiliation:
Department of Mathematics, University of Oslo, PO Box 1053 Blindern, NO-0316 Oslo, Norway
J. MONBALIU
Affiliation:
KU Leuven, Kastlepark Arenberg 40, 3001 Heverlee, Belgium
E. BITNER-GREGERSEN
Affiliation:
Det Norske Veritas, Veritasveien 1, NO-1322 Høvik, Norway
M. ONORATO
Affiliation:
Dipartimento di Fisica Generale, Università di Torino, Via P. Giuria 1, 10125 Torino, Italy
*
†Present address: Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, PO Box 218, Hawthorn, Victoria 3122, Australia. Email address for correspondence: [email protected]
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Abstract

Nonlinear modulational instability of wavepackets is one of the mechanisms responsible for the formation of large-amplitude water waves. Here, mechanically generated waves in a three-dimensional basin and numerical simulations of nonlinear waves have been compared in order to assess the ability of numerical models to describe the evolution of weakly nonlinear waves and predict the probability of occurrence of extreme waves within a variety of random directional wave fields. Numerical simulations have been performed following two different approaches: numerical integration of a modified nonlinear Schrödinger equation and numerical integration of the potential Euler equations based on a higher-order spectral method. Whereas the first makes a narrow-banded approximation (both in frequency and direction), the latter is free from bandwidth constraints. Both models assume weakly nonlinear waves. On the whole, it has been found that the statistical properties of numerically simulated wave fields are in good quantitative agreement with laboratory observations. Moreover, this study shows that the modified nonlinear Schrödinger equation can also provide consistent results outside its narrow-banded domain of validity.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 313 - 336
Copyright
Copyright © Cambridge University Press 2010

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References

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